Problem: Solve for $p$. $10p-3=2(12+4p)-7$ $p =$
Explanation: We need to manipulate the equation to get $ p $ by itself. $\begin{aligned} 10p-3 &= 2(12+4p)-7 \\\\ 10p-3 &= 24+8p-7~~~~~~~~~~\gray{\text{Distribute}}\\\\ 10p-3 &= 17+8p~~~~~~~~~~\gray{\text{Combine like terms}}\\\\ 10p-3{-8p} &= 17+8p{-8p} ~~~~~~~~~~\gray{\text{Subtract 8p from each side}}\\\\ 2p-3&=17 ~~~~~~~~~~\gray{\text{Combine like terms}}\\\\ 2p-3{+3} &=17 {+3} ~~~~~~~~~~\gray{\text{Add 3 to each side}}\\\\ 2p&=20 ~~~~~~~~~~\gray{\text{Combine like terms}}\\\\ \dfrac{2p}{{2}}&= \dfrac{20}{{2}}~~~~~~~~~~\gray{\text{Divide each side by 2}} \\\\ p &= {10} ~~~~~~~~~~\gray{\text{Simplify}}\\\\ \end{aligned}$ The answer: $ p = 10{ }~~~~~~~~$ [Let's check our work!]